ai rezolvarea pt 69 si 70
69) a*bc=a(10b+c)
b*ac= b(10a+c)
a*bc=b*ac+1
10ab+ac= 10ab+bc+1/-(10ab+bc)
10ab+ac-10ab-bc=1
ac-bc= 1
c(a-b)= 1
c=1, a-b= 1, a= 1+b
a= 1, b= 0, c= 1, abc= 101
a= 2, b= 1, c= 1, abc= 211
a= 3, b= 2, c= 1, abc= 321
a= 4, b= 3, c= 1, abc= 431
a= 5, b= 4, c= 1, abc= 541
a= 6, b= 5, c= 1, abc= 651
a= 7, b= 6, c= 1, abc= 761
a= 8, b= 7, c= 1, abc= 871
a= 9, b= 8, c= 1, abc= 981
M={101,211,321,431,541,651,761,871,981}
70) a) a= 1+2014+2014*2015= 2015+2014*2015=2015*(1+2014)= 2015*2015=2015^2 (patrat perfect)
b= 1+2014+2014*2015+2014*2015^2= 2015+2014*2015+2014*2015^2= 2015*(1+2014+2014*2015)= 2015*2015^2= 2015^3 (cub perfect)
din calculele facute pt determinarea lui a si b, rezulta ca A= 2016^2016= (2016^1008)^2 (patratul nr. 2016^1008)
A= 2016^2016= (2016^672)^3 (cubul nr. 2016^672)
